ADDMC: Weighted Model Counting with Algebraic Decision Diagrams

Dudek, Jeffrey M.; Phan, Vu H. N.; Vardi, Moshe Y.

doi:10.1609/aaai.v34i02.5505

Cited by 28 publications

(58 citation statements)

References 26 publications

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“…Overall the 99 solved instances compares favourably with the best score of 69 achieved in the competition [74]. For those 69 instances we confirmed all results against the ADDMC solver [75].…”

Section: Exact Weighted Model Countingsupporting

confidence: 66%

Hyper-optimized tensor network contraction

Gray

Kourtis

2021

Quantum

164

152

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Tensor networks represent the state-of-the-art in computational methods across many disciplines, including the classical simulation of quantum many-body systems and quantum circuits. Several applications of current interest give rise to tensor networks with irregular geometries. Finding the best possible contraction path for such networks is a central problem, with an exponential effect on computation time and memory footprint. In this work, we implement new randomized protocols that find very high quality contraction paths for arbitrary and large tensor networks. We test our methods on a variety of benchmarks, including the random quantum circuit instances recently implemented on Google quantum chips. We find that the paths obtained can be very close to optimal, and often many orders or magnitude better than the most established approaches. As different underlying geometries suit different methods, we also introduce a hyper-optimization approach, where both the method applied and its algorithmic parameters are tuned during the path finding. The increase in quality of contraction schemes found has significant practical implications for the simulation of quantum many-body systems and particularly for the benchmarking of new quantum chips. Concretely, we estimate a speed-up of over 10,000× compared to the original expectation for the classical simulation of the Sycamore `supremacy' circuits.

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Section: Exact Weighted Model Countingsupporting

confidence: 66%

Hyper-optimized tensor network contraction

Gray

Kourtis

2021

Quantum

164

152

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“…Probabilistic Graphical Models. There is a rich literature in optimizing the representation of probabilistic graphical models for faster inference (Chavira and Darwiche 2008;Darwiche 2009;Choi, Kisa, and Darwiche 2013;Dudek, Phan, and Vardi 2020;Dilkas and Belle 2021). Chavira and Darwiche (2008) optimize the encoding the discrete graphical models that exploits an analogous notion of duplicate flips.…”

Section: Related Workmentioning

confidence: 99%

flip-hoisting: Exploiting Repeated Parameters in Discrete Probabilistic Programs

Cheng

Millstein

Broeck

et al. 2021

Preprint

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Probabilistic programming is emerging as a popular and effective means of probabilistic modeling and an alternative to probabilistic graphical models. Probabilistic programs provide greater expressivity and flexibility in modeling probabilistic systems than graphical models, but this flexibility comes at a cost: there remains a significant disparity in performance between specialized Bayesian network solvers and probabilistic program inference algorithms. In this work we present a program analysis and associated optimization, flip-hoisting, that collapses repetitious parameters in discrete probabilistic programs to improve inference performance. flip-hoisting generalizes parameter sharing -a well-known important optimization from discrete graphical models -to probabilistic programs. We implement fliphoisting in an existing probabilistic programming language and show empirically that it significantly improves inference performance, narrowing the gap between the performances of probabilistic programs and probabilistic graphical models.

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“…Dynamic programming has also been the basis of several tools for model counting [25,26,27,31]. Although each tool uses a different data structurealgebraic decision diagrams (ADDs) [26], tensors [25,27], or database tables [31]the overall algorithms have similar structure. The goal of this work is to unify these approaches into a single conceptual framework: project-join trees.…”

Section: Introductionmentioning

confidence: 99%

“…We argue that project-join trees provide the natural formalism to describe execution plans for dynamic-programming algorithms for model counting. In particular, considering project-join trees as execution plans enables us to decompose dynamic-programming algorithms such as the one in [26] into two phases, following the breakdown in [27]: a planning phase and an execution phase. This enables us to study and compare different planning algorithms, different execution environments, and the interplay between planning and execution.…”

Section: Introductionmentioning

confidence: 99%

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DPMC: Weighted Model Counting by Dynamic Programming on Project-Join Trees

Dudek¹,

Phan²,

Vardi³

2020

Preprint

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We propose a unifying dynamic-programming framework to compute exact literal-weighted model counts of formulas in conjunctive normal form. At the center of our framework are project-join trees, which specify efficient project-join orders to apply additive projections (variable eliminations) and joins (clause multiplications). In this framework, model counting is performed in two phases. First, the planning phase constructs a project-join tree from a formula. Second, the execution phase computes the model count of the formula, employing dynamic programming as guided by the project-join tree. We empirically evaluate various methods for the planning phase and compare constraint-satisfaction heuristics with tree-decomposition tools. We also investigate the performance of different data structures for the execution phase and compare algebraic decision diagrams with tensors. We show that our dynamic-programming model-counting framework DPMC is competitive with the state-of-the-art exact weighted model counters Cachet, c2d, d4, and miniC2D.

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ADDMC: Weighted Model Counting with Algebraic Decision Diagrams

Cited by 28 publications

References 26 publications

Hyper-optimized tensor network contraction

Hyper-optimized tensor network contraction

flip-hoisting: Exploiting Repeated Parameters in Discrete Probabilistic Programs

DPMC: Weighted Model Counting by Dynamic Programming on Project-Join Trees

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